The Hidden Geometry of Complex, Network-Driven Contagion Phe

The Hidden Geometry of Complex, Network-Driven ContagionPhenomena

Dirk Brockmann and Dirk HelbingScience 342, 1337 (2013);

DOI: 10.1126/science.1245200

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TheHiddenGeometryofComplex,Network-DrivenContagionPhenomena

DirkBrockmann1,2,3*andDirkHelbing4,5

Theglobalspreadofepidemics,rumors,opinions,andinnovationsarecomplex,network-drivendynamicprocesses.Thecombinedmultiscalenatureandintrinsicheterogeneityoftheunderlying

networksmakeitdifficulttodevelopanintuitiveunderstandingoftheseprocesses,todistinguishrelevantfromperipheralfactors,topredicttheirtimecourse,andtolocatetheirorigin.However,weshowthatcomplexspatiotemporalpatternscanbereducedtosurprisinglysimple,homogeneouswavepropagationpatterns,ifconventionalgeographicdistanceisreplacedbyaprobabilisticallymotivatedeffective

distance.Inthecontextofglobal,air-traffic–mediatedepidemics,weshowthateffectivedistancereliablypredictsdiseasearrivaltimes.Evenifepidemiologicalparametersareunknown,themethodcanstilldeliverrelativearrivaltimes.Theapproachcanalsoidentifythespatialoriginofspreadingprocessesand

successfullybeappliedtodataoftheworldwide2009H1N1influenzapandemicand2003SARSepidemic.hegeographicspreadofemergentinfec-tiousdiseasesaffectsthelivesoftensofthousandsorevenmillionsofpeople(1,2).RecentexamplesofemergentdiseasesaretheSARSepidemicof2003,the2009H1N1influenzapandemic,andmostrecentlyanewstrain(H7N9)ofavianinfluenzavirus(3,4).Progressingworld-wideurbanization,combinedwithgrowingcon-nectivityamongmetropolitancenters,hasincreasedtheriskthathighlyvirulentemergentpathogenswillspread(5–8).Thecomplexityofglobalhu-manmobility,particularlyairtraffic(Fig.1A),makesitincreasinglydifficulttodevelopeffec-tivecontainmentandmitigationstrategiesonthetimescaleimposedbythespeedatwhichmod-erndiseasescanspread(9–11).Becausetimely,accurate,andfocusedactioncanpotentiallysavethelivesofmanypeopleandreducethesocio-economicimpactofinfectiousdiseases(12,13),understandingglobaldiseasedynamicshasbe-comeamajor21st-centurychallenge.Unravelingthecoremechanismsthatunderliethesephenome-naandbeingabletodistinguishkeyfactorsfromperipheralonesarerequiredtodevelopquantita-tive,efficient,andpredictivemodelsthatpublichealthauthoritiescanemploytoassesssituationsquickly,makeinformeddecisions,andoptimizevaccinationanddrugdeliveryplans.Afterthein-itialoutbreakofanepidemic,thekeyquestionsareasfollows:(i)Wheredidthenovelpathogenemerge?(ii)Wherearenewcasestobeexpected?(iii)Whenisanepidemicgoingtoarriveatdistantlocations?(iv)Howmanycasesaretobeexpected?

Historically,forcaseslikethespreadoftheBlackDeathinEurope,reaction-diffusionmod-12

T

Robert-Koch-Institute,Seestraße10,13353Berlin,Germany.InstituteforTheoreticalBiology,Humboldt-UniversityBerlin,Invalidenstraße42,10115Berlin,Germany.3DepartmentofEngineeringSciencesandAppliedMathematicsandNorthwesternInstituteonComplexSystems,NorthwesternUniversity,Evanston,IL60208,USA.4ETHZurich,SwissFederalInstituteofTechnology,CLUE1,Clausiusstraße50,8092Zurich,Switzerland.5RiskCen-ter,ETHZurich,Scheuchzerstraße7,8092Zurich,Switzerland.*Correspondingauthor.E-mail:dirk.brockmann@hu-berlin.de

elshavebeenquiteusefulinaddressingthesequestions(14,15).Despitetheirhighlevelofabstraction,thesemodelsprovideasolidintuitionandunderstandingofspreadingprocesses.Theirmathematicalsimplicitypermitstheassessmentofkeyproperties,e.g.,spreadingspeed,arrivaltimes,andhowpatterngeometrydependsonsys-temparameters(16).However,becauseoflong-distancetravel,simplereaction-diffusionmodelsareinadequateforthedescriptionoftoday’scom-plex,spatiallyincoherentspreadingpatternsthatgenericallybearnometricregularity,thatdependsensitivelyonmodelparametersandinitialcon-ditions(17–20)(Fig.1,BtoE,andfig.S2).Consequently,scientistshavebeendevelopingpowerful,large-scalecomputationalmodelsandsophisticated,parameter-richepidemicsimulatorsthattackletheabovekeyquestionsindetailedways.Theseconsiderdemographics,mobility,andepidemiologicaldata,aswellasdisease-specificmechanisms,allofwhicharebelievedtoplayarole(21–23).Modelsrangefromhigh-levelsto-chasticmetapopulationmodels(5,20,24)toagent-basedcomputersimulationsthataccountforthebehaviorandinteractionsofmillionsofindividualsinlargepopulations(25).Theseapproacheshavebecomeremarkablysuccessfulinreproducingob-servedpatternsandpredictingthetemporalevo-lutionofongoingepidemics(26).Manysuchmodelsreproducesimilardynamicfeaturesdespitemajordifferenc …… 此处隐藏：5985字，全部文档内容请下载后查看。喜欢就下载吧 ……